Out of four statements below, some statement(s) are correct and some are incorrect. If the sequence of their truth value is (say) $TFTT$ i.e.,  $S_1$ is True,  $S_2$ is False,  $S_3$ is True,  $S_4$ is True, then enter 1011 in response.(For e.g. if the sequence of their truth value is $FFTT$ then enter $0011=11,FTFF$ then enter $0100=100$ etc, $1=0001$ would mean $FFFT,101=0101$would mean $FTFT$ etc)

$S_1:\underset{x\to 0^{+}}{\lim }\frac{e^{x\ln x}-e^{\left[\cos x\right]}}{x\ln x}=0,$ where [ . ] represents greatest integer function.

$S_2$ : Given $\underset{x\to a}{\lim }(f\left(x\right)+g\left(x\right))and\underset{x\to a}{\lim }(f\left(x\right)-g\left(x\right))$ exist, then it is not necessary that $\underset{x\to a}{\lim }f\left(x\right)and\underset{x\to a}{\lim }g\left(x\right)$ both exist separately.

$S_3:$  The value of $\underset{x\to 0}{\lim }\frac{(1-\cos ax)}{x^2}$ is  $\frac{a^2}{4}$

$S_4$ : Given function $f:R-\left\{0\right\}\to R,f\left(x\right)=\frac{\left(\sin ax\right)(1-\cos 2ax)(e^{2x}-1)}{x^4}, a\in R$ then the value of $\underset{a\to 0}{\lim }\frac{\left(\sin ax\right)(1-\cos 2ax)(e^{2x}-1)}{x^4}$ is  $4a^3$

Write the correct sequence of the above four statements as per the given order...?